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# Hydraulic Calculations

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1. Hydraulic Calculations

2. Objectives • We will cover the following: • The basic formulas for calculating: • Determining pump discharge pressure • Determining flow • Calculating friction loss

3. It’s about the math • Yep it’s algebra, get over it • This is why your Mom and Dad told you to pay attention in school • I know most of you haven’t done math since you left school • I was worse at math than you

4. Too much time • Most guys will spend MOST of their time preparing for the Drivers test studying the math • Realistically it’s less than 30% of the test • It’s the most important 30% but still it’s only 30%

5. This is just a review • This is not an algebra course, we don’t have the time for that • It’s just a review of the formulas and a chance for us to make sure you are working them correctly

6. Pump Discharge Pressure • Pump discharge pressure is the SUM total of ALL losses • Friction loss • Nozzle pressure • Elevation loss • Appliance loss • Formula – PDP=NP+FL+EL+AL

7. Let’s start with Friction Loss

8. Friction Loss • Standard Calculation: • CQ2L • C=Coefficient (from chart) • Q=Flow (gpm/100) • L=Length (figured in 100 foot lengths)

9. Coefficients – (C) • These are the coefficients for the hose that WE use: • 1 ½” 24 • 1 ¾” 15.5 • 2 ½” 2 • 3” .8 • 5” .08 • There are more but they are for hose we either don’t have or use

10. How to determine flow – (Q) • There are three possibilities when it comes to Q: • Smooth bore nozzles have to be calculated based on tip size • Selectable gallon nozzles are determined by the selected flow • Automatic nozzles are determined desired flow

11. Calculating flow • Smooth bore formula: • 29.7 X D2 X √np • 29.7 is a constant • D2 is the nozzle tip size squared • Square root of the nozzle pressure • Hand lines – 7 • Master streams - 9

12. The constant • 29.7

13. Diameter squared • 1” tip • d=1, d2= 1 x 1 or 1 • 1 ½” tip • d=1.5, d2= 1.5 x 1.5 or 2.25 • 2” tip • d=2, d2= 2 x 2 or 4 • The principle is the same for ANY smooth bore orifice regardless of size

14. Square root of NP • If your calculator has a square root key you can use it • Or • Since hand line NP is 50 you can simply use 7 (square root of 49, which is really close) • And master streams NP is 80 you can use 9 (square root of 81, again it’s really close)

15. Example for finding (Q) • 29.7 x d2 x sq. rt. of NP • 1” tip on a 2 ½” smooth bore hand line • 29.7 x 1 x 7=207.9 • 207.9 gpm • This is the ACTUAL flow • 207.9 is not practical for calculation in the field so we round it off to 210 • IMPORTANT: for written testing the actual flow will have to be calculated do not round to more than 1 decimal place!

16. Rounded field flow • This is what we use in the field (also what your pump chart is based on) • 2 ½” hand lines • 1” 210gpm • 1 1/8” 265gpm • 1 ¼” 325gpm

17. Calculated and field flows • Master streams • 1 3/8” 505 (actual) 500gpm (rounded) • 1 ½” 591 (actual) 600gpm (rounded) • 1 ¾” 818 (actual) 800gpm (rounded) • 2” 1063 (actual) 1000gpm (rounded) • For ease of calculation and based on the fact that master streams are secured rounding to the above numbers is acceptable

18. Known Flow (Q) • For known flows from selectable gallonage nozzles • For automatic nozzles where you set the DESIRED gallonage • Example: • 1 ¾” nozzle SET at 125gpm • Automatic nozzle where 125gpm is desired

19. Determining Q • Q simply stands for quantity • In order to get Q to fit in the equation we have to work a formula to get a small number • Otherwise we would have a large number that is unwieldy • We simply divide GPM by 100 and then square the result

20. It’s really simple • Q=GPM/1002 • 125gpm/1002 • 125/100=1.25 • 1.25x1.25=1.56 (rounded to 2 decimal places) • Q=1.56

21. Length – (L) • This is the multiplier for your calculation of friction loss • Since all calculations are figured on 100 foot sections we need to have a way to distribute your work to the entire system • Each 100’ section gets a value of 1 • Example: 200’ of hose = 2

22. Putting it together • CQ2L=friction loss • 100 feet of 1 ½” hose flowing 125gpm • C=24 • Q2=1.56 • L=1 • 24 x 1.56 x 1 = 37.44 • Friction Loss is 37.44 psi per 100 foot section

23. Your turn • Try figuring the following: • 200gpm through 300’ 1 ¾” hose • 600gpm through 1000’ 5” hose • 300gpm through 500’ 3” hose • 250gpm through 200’ 2 ½” hose

24. 200gpm through 300’ 1 ¾” hose • CQ2 L • C=15.5 • Q=200/100 or 2 • Q2=2*2 or 4 • L=3 • 15.5*4*3=186 • FL for this hose lay is 186psi

25. 600gpm through 1000’ 5” hose • CQ2 L • C=.08 • Q=600/100 or 6 • Q2=6*6 or 36 • L=10 • .08*36*10=28.8 • FL for this hose lay is 28.8psi

26. 300gpm through 500’ 3” hose • CQ2 L • C=.8 • Q=300/100 or 3 • Q2=3*3 or 9 • L=5 • .8*9*5=36 • FL for this hose lay is 36psi

27. 250gpm through 200’ 2 ½” hose • CQ2 L • C=2 • Q=250/100 or 2.5 • Q2=2.5*2.5 or 6.25 • L=2 • 2*6.25*2=25 • FL for this hose lay is 25psi

28. Now let’s add the nozzles

29. Nozzle pressure • Fog nozzles (automatics are fog) • Hand lines 100psi • Master streams 100psi • Aerial Devices • Trucks 80psi • Ladder 100psi

30. Nozzle pressure • Smooth bore • Hand lines 50psi • Master streams 80psi • Mounted master streams 100psi

31. Elevation is next

32. Elevation Loss/Gain • A column of water 1 foot tall exerts .434psi at it’s base • We round this up to .5psi or ½ pound per foot • This pressure works either for us or against us

33. Elevation Gain (head pressure) • If we stay with the ½ pound per foot then we gain 5 pounds of force for every 10 feet • 10*.5=5 • Example – A 100 foot water tower generates 50psi head pressure at its base

34. Elevation Loss • If we have to move water up, the pressure is reversed • Elevation loss is ½ pound per foot • 100 feet of elevation = 50psi of loss

35. Buildings and EL • It’s just a little different, and really only applies to standpipes • Floor height is considered to be 10 feet • Multiply 10 feet by .5 and the result is 5 • Standard elevation loss is 5psi per floor (not including the first floor)

36. And finish with appliances

37. Appliance Loss • For flows under 350gpm 0psi • For flows over 350gpm 10psi • Master stream appliances 25psi • Trucks are the exception! • Truck 1,3 & 5 50psi

38. You try it • 200 feet 1 ¾” flowing 150gpm • 150 feet 2 ½” flowing 1 1/8” tip • 150 feet 1 ¾” flowing 125gpm • 800 feet of 5” flowing 1200gpm • 150 feet 1 ½” flowing 60gpm • 400 feet of 3” flowing 400gpm

39. 200 feet 1 ¾” flowing 150gpm • PDP = FL + NP (this is a known flow so it’s fog) • FL = CQ2L • C = 15.5 • Q2 = 1.52 or 2.25 • L = 2 • FL=15.5 x 2.25 x 2 or 69.75 • NP = 100 • PDP is 169.75 or 169.8

40. We need to find Q 1st Q = 29.7 x d2 x √NP 29.7 (constant) d2 = 1.1252 or 1.27 √NP = 7 (sqrt of 49) 29.7 x 1.27 x 7 = 264.03 264 (rounded)/100=2.64 2.6(rounded) Q = 2.6 PDP = FL + NP FL = CQ2L C = 2 Q2 = 2.62 or 6.76 L = 1.5 FL= 2 x 6.76 x 1.5 or 20.28 NP = 50 (handline) PDP is 70.28 or 70.3 150 feet 2 ½” flowing 1 1/8” tip

41. 150 feet 1 ¾” flowing 125gpm • PDP = FL + NP (this is a known flow so it’s fog) • FL = CQ2L • C = 15.5 • Q2 = 1.252 or 1.56 • L = 1.5 • FL=15.5 x 1.56 x 1.5 or 36.27 • NP = 100 • PDP is 136.27 or 136.3

42. 800 feet of 5” flowing 1200gpm • PDP = FL (there is no NP for this exercise) • FL = CQ2L • C = .08 • Q2 = 122 or 144 • L = 8 • FL=.08 x 144 x 8 = 92.16 • PDP is 92.16

43. 150 feet 1 ½” flowing 60gpm • PDP = FL + NP (this is a known flow so it’s fog) • FL = CQ2L • C = 24 • Q2 = .62 or .36 • L = 1.5 • FL=24 x .36 x 1.5 or 12.96 • NP = 100 • PDP is 112.96 or 113

44. 400 feet of 3” flowing 400gpm • PDP = FL (there is no NP for this exercise) • FL = CQ2L • C = .8 • Q2 = 42 or 16 • L = 4 • FL=.8 x 16 x 4 = 51.2 • PDP is 51.2

45. Complex hose lays

46. Complex hose lays • Complex hose lays are nothing more than a series of simple lays strung together • Complex lays are either wyed apart (flow is combined) or siamesed together (flow is divided) • Major concern with multiple lines is length, diameter and flow per line

47. Pressure is the killer • The reason we end up with complex lays is because of pressure • High GPM flows generally equal high pressure • The only way we reduce pressure is to reduce flow per line • The way we do that is by adding lines to divide the flow

48. Two things • The two factors we need to address are: • Maximum efficient flow • Percent of test pressure

49. Maximum efficient flow • While it is theoretically possible to flow water forever there are real limits to how far we can shove water and still have a usable stream • This is referred to as Maximum Efficient Flow (MEF)

50. Maximum efficient flow • MEF for 5” hose is 1200gpm • MEF for 3” hose is 500gpm • MEF for 2 ½” hose is 300gpm